[Segment Replication] Wait for segment replication to be completed and marked done before assertion

[dreamer-89]

Description

This change fixes the flakyness in testSegmentReplicationStatsResponse happening due to race condition where segment replication does not complete before fetching SegmentReplicationStatsResponse response. The change waits for segment replication to complete before assertions. The change also removes deprecated assertThat.

Sample unstable gradle check: https://build.ci.opensearch.org/job/gradle-check/11323/

Issues Resolved

#5669

Check List

• New functionality includes testing.
  • All tests pass
• New functionality has been documented.
  • New functionality has javadoc added
• Commits are signed per the DCO using --signoff
• Commit changes are listed out in CHANGELOG.md file (See: Changelog)

By submitting this pull request, I confirm that my contribution is made under the terms of the Apache 2.0 license.
For more information on following Developer Certificate of Origin and signing off your commits, please check here.

[github-actions]

Gradle Check (Jenkins) Run Completed with:

• RESULT: FAILURE ❌
• URL: https://build.ci.opensearch.org/job/gradle-check/11350/
• CommitID: 829df25
  Please examine the workflow log, locate, and copy-paste the failure(s) below, then iterate to green.
  Is the failure a flaky test unrelated to your change?

[github-actions]

Gradle Check (Jenkins) Run Completed with:

• RESULT: SUCCESS ✅
• URL: https://build.ci.opensearch.org/job/gradle-check/11352/
• CommitID: 3e40fa9

[codecov-commenter]

Codecov Report

Merging #6370 (3e40fa9) into main (1540e00) will increase coverage by 0.08%.
The diff coverage is n/a.

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@@             Coverage Diff              @@
##               main    #6370      +/-   ##
============================================
+ Coverage     70.67%   70.75%   +0.08%     
- Complexity    58948    59021      +73     
============================================
  Files          4800     4800              
  Lines        282421   282421              
  Branches      40719    40719              
============================================
+ Hits         199587   199817     +230     
+ Misses        66392    66174     -218     
+ Partials      16442    16430      -12     

Impacted Files	Coverage Δ
...gations/bucket/composite/CompositeAggregation.java	15.00% <0.00%> (-80.00%)	⬇️
...pensearch/client/cluster/RemoteConnectionInfo.java	0.00% <0.00%> (-68.30%)	⬇️
...a/org/opensearch/client/cluster/ProxyModeInfo.java	0.00% <0.00%> (-55.00%)	⬇️
...ch/transport/ReceiveTimeoutTransportException.java	50.00% <0.00%> (-50.00%)	⬇️
...cluster/coordination/PendingClusterStateStats.java	20.00% <0.00%> (-48.00%)	⬇️
.../org/opensearch/client/indices/AnalyzeRequest.java	31.00% <0.00%> (-45.00%)	⬇️
...ter/shards/TransportClusterSearchShardsAction.java	53.84% <0.00%> (-43.59%)	⬇️
.../opensearch/client/cluster/RemoteInfoResponse.java	61.53% <0.00%> (-38.47%)	⬇️
...aggregations/bucket/composite/ParsedComposite.java	44.44% <0.00%> (-37.04%)	⬇️
...n/decider/SnapshotInProgressAllocationDecider.java	34.78% <0.00%> (-34.79%)	⬇️
... and 497 more

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[opensearch-trigger-bot]

The backport to 2.x failed:

The process '/usr/bin/git' failed with exit code 128

To backport manually, run these commands in your terminal:

# Fetch latest updates from GitHub
git fetch
# Create a new working tree
git worktree add ../.worktrees/backport-2.x 2.x
# Navigate to the new working tree
pushd ../.worktrees/backport-2.x
# Create a new branch
git switch --create backport/backport-6370-to-2.x
# Cherry-pick the merged commit of this pull request and resolve the conflicts
git cherry-pick -x --mainline 1 eeb149fa03a951b74209d258c6d2d93ee366b087
# Push it to GitHub
git push --set-upstream origin backport/backport-6370-to-2.x
# Go back to the original working tree
popd
# Delete the working tree
git worktree remove ../.worktrees/backport-2.x

Then, create a pull request where the base branch is 2.x and the compare/head branch is backport/backport-6370-to-2.x.